Kenneth Rosen Edition 6th Exercise 1.1 Question 23 (Page No. 18)

Question

State the converse, contrapositive, and inverse of each of these conditional statements.

• A. If it snows today, I will ski tomorrow.
• B. I come to class whenever there is going to be a quiz.
• C. A positive integer is a prime only if it has no divisors other than 1 and itself.

Comments

But if the question is "A positive integer is prime only if it has no divisors other than 1 and itself ."

Since it is "only if " p:A positive integer is prime and q:it has no divisors other than 1 and itself

so converse - if it has no divisors other than 1 and itself then a positive integer is prime .

but answer in kenneth rozen is "If  a positive integer is prime then it has no divisors other than 1 and itself ."

How ? Can anyone explain me .

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@Ruchi Vora

No, in Kenneth Rosen given Answer is, 

A positive integer is a prime if it has no divisors other than 1 and itself.

Answer 1

• A. If it snows today, I will ski tomorrow.
• B. converse =if I will ski tomorrow ,it snows today.
• C. inverse=If it not snows today, I will not ski tomorrow.
• D. contrapositive = if I will not ski tomorrow ,it  not snows today.

 

Do same for other parts.

Answer 2

• A. If it snows today, I will ski tomorrow

Converse will be: I will ski tomorrow only if it snows today

Inverse: If it doesn’t snow today, I will not ski tomorrow

Contrapositive: If I don’t ski tomorrow, then it will not have snowed today

• A. I come to class whenever there is going to be a quiz.

Converse: If I come to class, then there will be a quiz

Inverse: If there is not going to be a quiz, then I don’t come to class

Contrapositive: If I don’t come to class then there won’t be a quiz

100. A positive integer is a prime only if it has no divisors other than 1 and itself.

Converse: If a positive integer has no divisors other than 1 and itself then it is prime.

Inverse: If a positive integer is not prime then it has divisors other than 1 and itself.

Contrapositive: If a positive integer has divisors other than 1 and itself then it is not a prime.

Answer 3

The converse of "If it snows today, I will ski tomorrow" is "If I ski tomorrow, it snows today". The contrapositive of "If it snows today, I will ski tomorrow" is "If I do not ski tomorrow, it does not snow today". The inverse of "If it snows today, I will ski tomorrow" is "If it does not snow today, I will not ski tomorrow".

The converse of "I come to class whenever there is going to be a quiz" is "If I come to class, there is going to be a quiz". The contrapositive of "I come to class whenever there is going to be a quiz" is "If I do not come to class, there is not going to be a quiz". The inverse of "I come to class whenever there is going to be a quiz" is "I do not come to class whenever there is not going to be a quiz".

The converse of "A positive integer is a prime only if it has no divisors other than 1 and itself" is "If a positive integer has no divisors other than 1 and itself, then it is a prime". The contrapositive of "A positive integer is a prime only if it has no divisors other than 1 and itself" is "If a positive integer is not a prime, then it has divisors other than 1 and itself". The inverse of "A positive integer is a prime only if it has no divisors other than 1 and itself" is "A positive integer is not a prime only if it has divisors other than 1 and itself".